Stability of a model for the Belousov-Zhabotinskij reaction

Vladimír Haluška

Aplikace matematiky (1989)

  • Volume: 34, Issue: 2, page 89-104
  • ISSN: 0862-7940

Abstract

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The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set.

How to cite

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Haluška, Vladimír. "Stability of a model for the Belousov-Zhabotinskij reaction." Aplikace matematiky 34.2 (1989): 89-104. <http://eudml.org/doc/15567>.

@article{Haluška1989,
abstract = {The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set.},
author = {Haluška, Vladimír},
journal = {Aplikace matematiky},
keywords = {Field-Körös-Noyes’ model; Belousov-Zhabotinskij reaction; Lyapunov function; equilibrium point; stability in the large; Field-Körös-Noyes’ model; Belousov-Zhabotinskij reaction; Lyapunov function},
language = {eng},
number = {2},
pages = {89-104},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stability of a model for the Belousov-Zhabotinskij reaction},
url = {http://eudml.org/doc/15567},
volume = {34},
year = {1989},
}

TY - JOUR
AU - Haluška, Vladimír
TI - Stability of a model for the Belousov-Zhabotinskij reaction
JO - Aplikace matematiky
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 2
SP - 89
EP - 104
AB - The paper deals with the Field-Körös-Noyes' model of the Belousov-Yhabotinskij reaction. By means of the method of the Ljapunov function a sufficient condition is determined that the non-trivial critical point of this model be asymptotically stable with respect to a certain set.
LA - eng
KW - Field-Körös-Noyes’ model; Belousov-Zhabotinskij reaction; Lyapunov function; equilibrium point; stability in the large; Field-Körös-Noyes’ model; Belousov-Zhabotinskij reaction; Lyapunov function
UR - http://eudml.org/doc/15567
ER -

References

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  1. K. Bachratý, On the stability of a model for the Belousov-Zhabotinskij reaction, Acta mathematica Univ. Comen. XLII-XLIII (2983), 225-234. Zbl0619.34055MR0740754
  2. R. J. Field R. M. Noyes, 10.1063/1.1681288, J. Chem. Phys. 60 (1974), 1877-1884. (1974) DOI10.1063/1.1681288
  3. P. Hartman, Ordinary Differential Equations, J. Wiley and Sons, New York-London-Sydney (1964) (Russian translation, Izdat Mir, Moskva, 1970). (1964) Zbl0125.32102MR0171038
  4. I. D. Hsü, Existence of periodic solutions for the Belousov-Zaikin-Zhabotinskij reaction by a theorem of Hopf, J. Differential Equations 20 (1976), 339-403. (1976) MR0457858
  5. J. La Salle S. Lefschetz, Stability by Liapunov'z Direct method with applications, Academic Press, New York-London (2961) (Russian translation, Izdat. Mir, Moskva, 1964). (1964) 
  6. J. D. Murray, On a model for temporal oscillations in the Belousov-Zhabotinskij reaction, J. Chem. Phys. 6 (1975), 3610-3613. (1975) 
  7. G. Streng, Linear algebra and its applications, Academic Press, New York (1976) (Russian translation, Izdat. Mir, Moskva, 1980). (1976) 
  8. V. Šeda, On the existence of oscillatory solutions in the Weisbuch-Salomon-Atlan model for the Belousov-Zhabotinskij reaction, Apl. Mat. 23 (2978), 280-294. Zbl0405.34048MR0495430
  9. Y. Takeuchi N. Adachi H. Tokumaru, The stability of generalized Volterra equations, J. Math. anal. Appl. 62 (2978), 453-473. Zbl0388.45011MR0477317
  10. J. J. Tyson, The Belousov-Zhabotinskij reaction, Lecture Notes in Biomathematics, Springer-Verlag, Berlin-Heidelberg-New York (1916). (1916) 

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